Christoffelsymbole

$Γ_{μ ν}^{α} = \frac{1}{2} g^{α σ} (g_{σ μ, ν} + g_{σ ν, μ} - g_{μ ν, σ})$

Γ_{μ ν}^{α} = \frac{\partial x^{α}}{\partial ξ^{β}} \frac{\partial^{2} ξ^{β}}{\partial x^{μ} \partial x^{ν}}

Verhalten bei Koordinatentransformation

Γ'_{μ ν}^{α} = \frac{\partial x'^{α}}{\partial x^{β}} \frac{\partial x^{ρ}}{\partial x'^{μ}} \frac{\partial x^{σ}}{\partial x'^{ν}} Γ_{ρ σ}^{β} + \frac{\partial x'^{α}}{\partial x^{β}} \frac{\partial^{2} x^{β}}{\partial x'^{μ} \partial x'^{ν}}